Non-hydrostatic model for internal wave generations and propagations using immersed boundary method

Abstract

A non-hydrostatic model is developed to predict internal wave generations and propagations. The model employs a semi-implicit, fractional step algorithm to solve the governing equations based on the Cartesian grid system. Immersed boundary method is incorporated to deal with the complex geometry of uneven bottoms. The combination of the z-level vertical coordinate and the immersed boundary method enables the model to treat uneven bottoms and meanwhile to avoid numerical errors in the calculation of the baroclinic pressure force. To consider the effect of stratification, a variant of the Smagorinsky sub-grid scale model is employed to calculate the eddy viscosity and diffusivity. The capability of the model in resolving internal wave generation by tidal forcing over an idealized Gaussian-shaped topography is firstly validated by comparing the developed model with a terrain-following non-hydrostatic model. Then, two laboratory-scale test cases involving internal solitary wave propagations over variable topographies are considered. It can be found that the model captures the main characteristics of waveform evolution including internal hydraulic jump, wave breaking and waveform inversion. Thus, the proposed model provide an alternative to simulate internal wave generations and propagations.